The duo, who entered into a civil partnership agreement in December 2005, had hoped to be allowed to adopt the 17-month-old Lev from an orphanage.
However, their civil partnership is not recognised under Ukrainian law. Also, under the country's law the 62-year-old Elton is too old for adopting a kid. Thus, John and Furnish, 47, have been offered to play guardians for Lev.
"We want to support Lev and his brother and get them into a Ukrainian home and out of the orphanage," the Sun quoted Furnish, as saying.
He said: "We were upset not to be allowed to adopt but we'll fight and work with the Ukrainian government to change the law so that HIV positive children can be adopted. We'll be like uncles. They can visit us on holidays."
He said John and he would weigh their options during the Christmas break. "That's part of what Christmas will be about - a chance to get off the treadmill and chill out. There is a lot for us to talk about," Furnish said.